# Infinity

**Infinity**

You are encouraged to solve this task according to the task description, using any language you may know.

- Task

Write a function which tests if infinity is supported for floating point numbers (this step should be omitted for languages where the language specification already demands the existence of infinity, e.g. by demanding IEEE numbers), and if so, returns positive infinity. Otherwise, return the largest possible positive floating point number.

For languages with several floating point types, use the type of the literal constant **1.5** as floating point type.

- Related task

## Contents

- 1 ActionScript
- 2 Ada
- 3 ALGOL 68
- 4 Argile
- 5 AWK
- 6 BBC BASIC
- 7 C
- 8 C#
- 9 C++
- 10 Clojure
- 11 CoffeeScript
- 12 Common Lisp
- 13 Component Pascal
- 14 D
- 15 Delphi
- 16 Dyalect
- 17 E
- 18 Eiffel
- 19 Erlang
- 20 ERRE
- 21 Euphoria
- 22 F#
- 23 Factor
- 24 Fantom
- 25 Forth
- 26 Fortran
- 27 FreeBASIC
- 28 GAP
- 29 Go
- 30 Groovy
- 31 Haskell
- 32 Icon and Unicon
- 33 IDL
- 34 Io
- 35 J
- 36 Java
- 37 JavaScript
- 38 jq
- 39 Julia
- 40 Lingo
- 41 Lua
- 42 K
- 43 Kotlin
- 44 Langur
- 45 Lasso
- 46 M2000 Interpreter
- 47 Maple
- 48 Mathematica / Wolfram Language
- 49 MATLAB / Octave
- 50 Maxima
- 51 Metafont
- 52 Modula-2
- 53 Modula-3
- 54 Nemerle
- 55 Nim
- 56 NS-HUBASIC
- 57 OCaml
- 58 Oforth
- 59 Ol
- 60 OpenEdge/Progress
- 61 OxygenBasic
- 62 Oz
- 63 PARI/GP
- 64 Pascal
- 65 Perl
- 66 Perl 6
- 67 Phix
- 68 PHP
- 69 PL/I
- 70 PicoLisp
- 71 PostScript
- 72 PowerShell
- 73 PureBasic
- 74 Python
- 75 R
- 76 Racket
- 77 REXX
- 78 RLaB
- 79 Ruby
- 80 Rust
- 81 Scala
- 82 Scheme
- 83 Seed7
- 84 Sidef
- 85 Slate
- 86 Smalltalk
- 87 Standard ML
- 88 Swift
- 89 Tcl
- 90 TI-89 BASIC
- 91 TorqueScript
- 92 Trith
- 93 Ursa
- 94 Ursala
- 95 Visual Basic
- 96 Yabasic
- 97 zkl
- 98 ZX Spectrum Basic

## ActionScript[edit]

ActionScript has the built in function isFinite() to test if a number is finite or not.

trace(5 / 0); // outputs "Infinity"

trace(isFinite(5 / 0)); // outputs "false"

## Ada[edit]

with Ada.Text_IO; use Ada.Text_IO;

procedure Infinities is

function Sup return Float is -- Only for predefined types

Result : Float := Float'Last;

begin

if not Float'Machine_Overflows then

Result := Float'Succ (Result);

end if;

return Result;

end Sup;

function Inf return Float is -- Only for predefined types

Result : Float := Float'First;

begin

if not Float'Machine_Overflows then

Result := Float'Pred (Result);

end if;

return Result;

end Inf;

begin

Put_Line ("Supremum" & Float'Image (Sup));

Put_Line ("Infimum " & Float'Image (Inf));

end Infinities;

The language-defined attribute Machine_Overflows is defined for each floating-point type. It is true when an overflow or divide-by-zero results in Constraint_Error exception propagation. When the underlying machine type is incapable to implement this semantics the attribute is false. It is to expect that on the machines with IEEE 754 hardware Machine_Overflows is true. The language-defined attributes Succ and Pred yield the value next or previous to the argument, correspondingly.

Sample output on a machine where Float is IEEE 754:

Supremum +Inf******* Infimum -Inf*******

Note that the code above does not work for user-defined types, which may have range of values narrower than one of the underlying hardware type. This case represents one of the reasons why Ada programmers are advised not to use predefined floating-point types. There is a danger that the implementation of might be IEEE 754, and so the program semantics could be broken.

Here is the code that should work for any type on any machine:

with Ada.Text_IO; use Ada.Text_IO;

procedure Infinities is

type Real is digits 5 range -10.0..10.0;

function Sup return Real is

Result : Real := Real'Last;

begin

return Real'Succ (Result);

exception

when Constraint_Error =>

return Result;

end Sup;

function Inf return Real is

Result : Real := Real'First;

begin

return Real'Pred (Result);

exception

when Constraint_Error =>

return Result;

end Inf;

begin

Put_Line ("Supremum" & Real'Image (Sup));

Put_Line ("Infimum " & Real'Image (Inf));

end Infinities;

Sample output. Note that the compiler is required to generate Constraint_Error even if the hardware is IEEE 754. So the upper and lower bounds are 10.0 and -10.0:

Supremum 1.0000E+01 Infimum -1.0000E+01

### Getting rid of IEEE ideals[edit]

There is a simple way to strip IEEE 754 ideals (non-numeric values) from a predefined floating-point type such as Float or Long_Float:

subtype Safe_Float is Float range Float'Range;

The subtype Safe_Float keeps all the range of Float, yet behaves properly upon overflow, underflow and zero-divide.

## ALGOL 68[edit]

ALGOL 68R (from Royal Radar Establishment) has an *infinity* variable as part of the *standard prelude*, on the ICL 1900 Series mainframes the value of *infinity* is 5.79860446188₁₀76 (the same as *max float*).

Note: The underlying hardware may sometimes support an infinity, but the ALGOL 68 standard itself does not, and gives no way of setting a variable to either ±∞.

ALGOL 68 does have some 7 built in exceptions, these might be used to detect exceptions during transput, and so __if__ the underlying hardware __does__ support ∞, then it would be detected with a *on value error* while printing and if *mended* would appear as a field full of *error char*.

printf(($"max int: "gl$,max int));

printf(($"long max int: "gl$,long max int));

printf(($"long long max int: "gl$,long long max int));

printf(($"max real: "gl$,max real));

printf(($"long max real: "gl$,long max real));

printf(($"long long max real: "gl$,long long max real));

printf(($"error char: "gl$,error char))

Output:

max int: +2147483647 long max int: +99999999999999999999999999999999999 long long max int: +9999999999999999999999999999999999999999999999999999999999999999999999 max real: +1.79769313486235e+308 long max real: +1.000000000000000000000000e+999999 long long max real: +1.00000000000000000000000000000000000000000000000000000000000e+999999 error char: *

## Argile[edit]

(simplified)use std

printf "%f\n" atof "infinity" (: this prints "inf" :)

#extern :atof<text>: -> real

## AWK[edit]

BEGIN {

k=1;

while (2^(k-1) < 2^k) k++;

INF = 2^k;

print INF;

}

This has been tested with GAWK 3.1.7 and MAWK, both return

inf

## BBC BASIC[edit]

*FLOAT 64

PRINT FNinfinity

END

DEF FNinfinity

LOCAL supported%, maxpos, prev, inct

supported% = TRUE

ON ERROR LOCAL supported% = FALSE

IF supported% THEN = 1/0

RESTORE ERROR

inct = 1E10

REPEAT

prev = maxpos

inct *= 2

ON ERROR LOCAL inct /= 2

maxpos += inct

RESTORE ERROR

UNTIL maxpos = prev

= maxpos

Output:

1.79769313E308

## C[edit]

A previous solution used `atof("infinity")`, which returned infinity with some C libraries but returned zero with MinGW.

C89 has a macro HUGE_VAL in <math.h>. HUGE_VAL is a `double`. HUGE_VAL will be infinity if infinity exists, else it will be the largest possible number. HUGE_VAL is a `double`.

#include <math.h> /* HUGE_VAL */

#include <stdio.h> /* printf() */

double inf(void) {

return HUGE_VAL;

}

int main() {

printf("%g\n", inf());

return 0;

}

The output from the above program might be "inf", "1.#INF", or something else.

C99 also has a macro for infinity:

#define _ISOC99_SOURCE

#include <math.h>

#include <stdio.h>

int main() {

printf("%g\n", INFINITY);

return 0;

}

## C#[edit]

using System;

class Program

{

static double PositiveInfinity()

{

return double.PositiveInfinity;

}

static void Main()

{

Console.WriteLine(PositiveInfinity());

}

}

Output:

Infinity

## C++[edit]

#include <limits>

double inf()

{

if (std::numeric_limits<double>::has_infinity)

return std::numeric_limits<double>::infinity();

else

return std::numeric_limits<double>::max();

}

## Clojure[edit]

Java's floating-point types (float, double) all support infinity. Clojure has literals for infinity:

##Inf ;; same as Double/POSITIVE_INFINITY

##-Inf ;; same as Double/NEGATIVE_INFINITY

(Double/isInfinite ##Inf) ;; true

The largest possible number in Java (without using the Big classes) is also in the Double class (def biggestNumber Double/MAX_VALUE). Its value is (1+(1-2^(-52)))*2^1023 or 1.7976931348623157*10^308 (a.k.a. "big"). Other number classes (Integer, Long, Float, Byte, and Short) have maximum values that can be accessed in the same way.

## CoffeeScript[edit]

CoffeeScript compiles to JavaScript, and as such it inherits the properties of JavaScript.

JavaScript has a special global property called "Infinity":

`Infinity`

as well as constants in the Number class:

Number.POSITIVE_INFINITY

Number.NEGATIVE_INFINITY

The global isFinite function tests for finiteness:

isFinite x

## Common Lisp[edit]

Common Lisp does not specify an infinity value. Some implementations may have support for IEEE infinity, however. For instance, CMUCL supports IEEE Special Values. Common Lisp does specify that implementations define constants with most (and least) positive (and negative) values. These may vary between implementations.

5.1.2, Intel, OS X, 32-bit> (apropos "MOST-POSITIVE" :cl)

MOST-POSITIVE-LONG-FLOAT, value: 1.7976931348623158D308

MOST-POSITIVE-SHORT-FLOAT, value: 3.4028172S38

MOST-POSITIVE-SINGLE-FLOAT, value: 3.4028235E38

MOST-POSITIVE-DOUBLE-FLOAT, value: 1.7976931348623158D308

MOST-POSITIVE-FIXNUM, value: 536870911

> (apropos "MOST-NEGATIVE" :cl)

MOST-NEGATIVE-SINGLE-FLOAT, value: -3.4028235E38

MOST-NEGATIVE-LONG-FLOAT, value: -1.7976931348623158D308

MOST-NEGATIVE-SHORT-FLOAT, value: -3.4028172S38

MOST-NEGATIVE-DOUBLE-FLOAT, value: -1.7976931348623158D308

MOST-NEGATIVE-FIXNUM, value: -536870912

## Component Pascal[edit]

BlackBox Component Builder

MODULE Infinity;

IMPORT StdLog;

PROCEDURE Do*;

VAR

x: REAL;

BEGIN

x := 1 / 0;

StdLog.String("x:> ");StdLog.Real(x);StdLog.Ln

END Do;

Execute: ^Q Infinity.Do

Output:

x:> inf

## D[edit]

auto inf() {

return typeof(1.5).infinity;

}

void main() {}

## Delphi[edit]

Delphi defines the following constants in Math:

Infinity = 1.0 / 0.0;

NegInfinity = -1.0 / 0.0;

Test for infinite value using:

Math.IsInfinite()

## Dyalect[edit]

Dyalect floating point number support positive infinity:

func infinityTask() {

Float.inf

}

## E[edit]

def infinityTask() {

return Infinity # predefined variable holding positive infinity

}

## Eiffel[edit]

class

APPLICATION

inherit

ARGUMENTS

create

make

feature {NONE} -- Initialization

number:REAL_64

make

-- Run application.

do

number := 2^2000

print(number)

print("%N")

print(number.is_positive_infinity)

print("%N")

end

end

Output:

Infinity True

## Erlang[edit]

No infinity available. Largest floating point number is supposed to be 1.80e308 (IEEE 754-1985 double precision 64 bits) but that did not work. However 1.79e308 is fine, so max float is somewhere close to 1.80e308.

## ERRE[edit]

Every type has its "infinity" constant: MAXINT for 16-bit integer, MAXREAL for single precision floating and MAXLONGREAL for double precision floating. An infinity test can be achieved with an EXCEPTION:

PROGRAM INFINITY

EXCEPTION

PRINT("INFINITY")

ESCI%=TRUE

END EXCEPTION

BEGIN

ESCI%=FALSE

K=1

WHILE 2^K>0 DO

EXIT IF ESCI%

K+=1

END WHILE

END PROGRAM

## Euphoria[edit]

constant infinity = 1E400

? infinity -- outputs "inf"

## F#[edit]

printfn "%f" (1.0/0.0)

- Output:

Infinity

## Factor[edit]

1/0.

## Fantom[edit]

Fantom's `Float`

data type is an IEEE 754 64-bit floating point type. Positive infinity is represented by the constant `posInf`

.

class Main

{

static Float getInfinity () { Float.posInf }

public static Void main () { echo (getInfinity ()) }

}

## Forth[edit]

: inf ( -- f ) 1e 0e f/ ;

inf f. \ implementation specific. GNU Forth will output "inf"

: inf? ( f -- ? ) s" MAX-FLOAT" environment? drop f> ;

\ IEEE infinity is the only value for which this will return true

: has-inf ( -- ? ) ['] inf catch if false else inf? then ;

## Fortran[edit]

ISO Fortran 2003 or later supports an IEEE_ARITHMETIC module which defines a wide range of intrinsic functions and types in support of IEEE floating point formats and arithmetic rules.

program to_f_the_ineffable

use, intrinsic :: ieee_arithmetic

integer :: i

real dimension(2) :: y, x = (/ 30, ieee_value(y,ieee_positive_inf) /)

do i = 1, 2

if (ieee_support_datatype(x(i))) then

if (ieee_is_finite(x(i))) then

print *, 'x(',i,') is finite'

else

print *, 'x(',i,') is infinite'

end if

else

print *, 'x(',i,') is not in an IEEE-supported format'

end if

end do

end program to_f_the_ineffable

ISO Fortran 90 or later supports a HUGE intrinsic which returns the largest value supported by the data type of the number given.

real :: x

real :: huge_real = huge(x)

## FreeBASIC[edit]

' FB 1.05.0 Win64

#Include "crt/math.bi"

#Print Typeof(1.5) ' Prints DOUBLE at compile time

Dim d As Typeof(1.5) = INFINITY

Print d; " (String representation of Positive Infinity)"

Sleep

- Output:

1.#INF (String representation of Positive Infinity)

## GAP[edit]

# Floating point infinity

inf := FLOAT_INT(1) / FLOAT_INT(0);

IS_FLOAT(inf);

#true;

# GAP has also a formal ''infinity'' value

infinity in Cyclotomics;

# true

## Go[edit]

package main

import (

"fmt"

"math"

)

// function called for by task

func posInf() float64 {

return math.Inf(1) // argument specifies positive infinity

}

func main() {

x := 1.5 // type of x determined by literal

// that this compiles demonstrates that PosInf returns same type as x,

// the type specified by the task.

x = posInf() // test function

fmt.Println(x, math.IsInf(x, 1)) // demonstrate result

}

Output:

+Inf true

## Groovy[edit]

Groovy, like Java, requires full support for IEEE 32-bit (Float) and 64-bit (Double) formats. So the solution function would simply return either the Float or Double constant encoded as IEEE infinity.

def biggest = { Double.POSITIVE_INFINITY }

Test program:

println biggest()

printf ( "0x%xL \n", Double.doubleToLongBits(biggest()) )

Output:

Infinity 0x7ff0000000000000L

## Haskell[edit]

The Haskell 98 standard does not require full IEEE numbers, and the required operations on floating point numbers leave some degree of freedom to the implementation. Also, it's not possible to use the type of the literal 1.0 to decide which concrete type to use, because Haskell number literals are automatically converted.

Nevertheless, the following may come close to the task description:

maxRealFloat :: RealFloat a => a -> a

maxRealFloat x = encodeFloat b (e-1) `asTypeOf` x where

b = floatRadix x - 1

(_,e) = floatRange x

infinity :: RealFloat a => a

infinity = if isInfinite inf then inf else maxRealFloat 1.0 where

inf = 1/0

Test for the two standard floating point types:

*Main> infinity :: Float

Infinity

*Main> infinity :: Double

Infinity

Or you can simply use division by 0:

Prelude> 1 / 0 :: Float

Infinity

Prelude> 1 / 0 :: Double

Infinity

Or use "read" to read the string representation:

Prelude> read "Infinity" :: Float

Infinity

Prelude> read "Infinity" :: Double

Infinity

## Icon and Unicon[edit]

Icon and Unicon have no infinity value (or defined maximum or minimum values). Reals are implemented as C doubles and the behavior could vary somewhat from platform to platform. Both explicitly check for divide by zero and treat it as a runtime error (201), so it's not clear how you could produce one with the possible exception of externally called code.

## IDL[edit]

IDL provides the standard IEEE values for _inf and _NaN in the !Values system structure:

print, !Values.f_infinity ;; for normal floats or

print, !Values.D_infinity ;; for doubles

## Io[edit]

inf := 1/0

or

`Number constants inf`

## J[edit]

Positive infinity is produced by the primary constant function` _: `.

It is also represented directly as a numeric value by an underscore, used alone.

Example:

_ * 5 NB. multiplying infinity to 5 results in infinity

_

5 % _ NB. dividing 5 by infinity results in 0

0

5 % 0 NB. dividing 5 by 0 results in infinity

_

## Java[edit]

Java's floating-point types (`float`, `double`) all support infinity. You can get infinity from constants in the corresponding wrapper class; for example, `Double`:

double infinity = Double.POSITIVE_INFINITY; //defined as 1.0/0.0

Double.isInfinite(infinity); //true

As a function:

public static double getInf(){

return Double.POSITIVE_INFINITY;

}

The largest possible number in Java (without using the `Big` classes) is also in the `Double` class.

double biggestNumber = Double.MAX_VALUE;

Its value is (2-2^{-52})*2^{1023} or 1.7976931348623157*10^{308} (a.k.a. "big"). Other number classes (`Integer`, `Long`, `Float`, `Byte`, and `Short`) have maximum values that can be accessed in the same way.

## JavaScript[edit]

JavaScript has a special global property called "Infinity":

`Infinity`

as well as constants in the Number class:

Number.POSITIVE_INFINITY

Number.NEGATIVE_INFINITY

The global isFinite() function tests for finiteness:

isFinite(x)

## jq[edit]

jq uses IEEE 754 64-bit floating-point arithmetic, and very large number literals, e.g. 1e1000, are evaluated as IEEE 754 infinity. If your version of jq does not include `infinite` as a built-in, you could therefore define it as follows:

def infinite: 1e1000;

To test whether a JSON entity is equal to `infinite`, one can simply use `==` in the expected manner. Thus, assuming `infinite` has been defined, one could define a predicate, isinfinite, as follows:

def isinfinite: . == infinite;

Currently, the infinite value prints as though it were a very large floating point number.

## Julia[edit]

Julia uses IEEE floating-point arithmetic and includes a built-in constant `Inf` for (64-bit) floating-point infinity.

infinity() = Inf

There is actually a built-in function that does returns infinity in various types, called `inf`, which takes as its argument the type to return infinity for.

inf(Float64) # 64-bit Inf

inf(Float32) # 32-bit Inf32

inf(BigFloat) # infinity for arbitrary-precision floating-point arithmetic

## Lingo[edit]

Lingo stores floats using IEEE 754 double-precision (64-bit) format. INF is not a constant that can be used programmatically, but only a special return value.

x = (1-power(2, -53)) * power(2, 1023) * 2

put ilk(x), x

-- #float 1.79769313486232e308

x = (1-power(2, -53)) * power(2, 1023) * 3

put ilk(x), x, -x

-- #float INF -INF

## Lua[edit]

function infinity()

return 1/0 --lua uses unboxed C floats for all numbers

end

## K[edit]

K has predefined positive and negative integer and float infinities: -0I, 0I, -0i, 0i. They have following properties:

/ Integer infinities

/ 0I is just 2147483647

/ -0I is just -2147483647

/ -2147483648 is a special "null integer"(NaN) 0N

0I*0I

1

0I-0I

0

0I+1

0N

0I+2

-0I

0I+3 / -0I+1

-2147483646

0I-1

2147483646

0I%0I

1

0I^2

4.611686e+18

0I^0I

0i

0I^-0I

0.0

1%0

0I

0%0

0

0i^2

0i

0i^0i

0i

/ Floating point infinities in K are something like

/ IEEE 754 values

/ Also there is floating point NaN -- 0n

0i+1

0i

0i*0i

0i

0i-0i

0n

0i%0i

0n

0i%0n

0n

/ but

0.0%0.0

0.0

## Kotlin[edit]

fun main(args: Array<String>) {

val p = Double.POSITIVE_INFINITY // +∞

println(p.isInfinite()) // true

println(p.isFinite()) // false

println("${p < 0} ${p > 0}") // false true

val n = Double.NEGATIVE_INFINITY // -∞

println(n.isInfinite()) // true

println(n.isFinite()) // false

println("${n < 0} ${n > 0}") // true false

}

- Output:

true false false true true false true false

## Langur[edit]

val .isPosInf = f isInfinity(.i) and isPosNumType(.i)

val .x = Infinity

val .y = -Infinity

val .z = 1

writeln ".x: ", .x, ": ", .isPosInf(.x)

writeln ".y: ", .y, ": ", .isPosInf(.y)

writeln ".z: ", .z, ": ", .isPosInf(.z)

- Output:

.x: Infinity: true .y: -Infinity: false .z: 1: false

## Lasso[edit]

Lasso supports 64-bit decimals.. This gives Lasso's decimal numbers a range from approximately negative to positive 2x10^300 and with precision down to 2x10^-300. Lasso also supports decimal literals for NaN (not a number) as well and positive and negative infinity.

infinity

'<br />'

infinity -> type

-> inf

decimal

## M2000 Interpreter[edit]

Rem : locale 1033

Module CheckIt {

Form 66,40

Cls 5

Pen 14

\\ Ensure True/False for Print boolean (else -1/0)

\\ from m2000 console use statement Switches without Set.

\\ use Monitor statement to see all switches.

Set Switches "+SBL"

IF version<9.4 then exit

IF version=9.4 and revision<25 then exit

Function Infinity(positive=True) {

buffer clear inf as byte*8

m=0x7F

if not positive then m+=128

return inf, 7:=m, 6:=0xF0

=eval(inf, 0 as double)

}

K=Infinity(false)

L=Infinity()

Function TestNegativeInfinity(k) {

=str$(k, 1033) = "-1.#INF"

}

Function TestPositiveInfinity(k) {

=str$(k, 1033) = "1.#INF"

}

Function TestInvalid {

=str$(Number, 1033) = "-1.#IND"

}

Pen 11 {Print " True True"}

Print TestNegativeInfinity(K), TestPositiveInfinity(L)

Pen 11 {Print " -1.#INF 1.#INF -1.#INF 1.#INF -1.#INF 1.#INF"}

Print K, L, K*100, L*100, K+K, L+L

M=K/L

Pen 11 {Print " -1.#IND -1.#IND True True" }

Print K/L, L/K, TestInvalid(M), TestInvalid(K/L)

M=K+L

Pen 11 {Print " -1.#IND -1.#IND -1.#IND True True"}

Print M, K+L, L+K, TestInvalid(M), TestInvalid(K+L)

Pen 11 {Print " -1.#INF 1.#INF"}

Print 1+K+2, 1+L+2

Pen 11 {Print " -1.#INF"}

Print K-L

Pen 11 {Print " 1.#INF"}

Print L-K

}

Checkit

## Maple[edit]

Maple's floating point numerics are a strict extension of IEEE/754 and IEEE/854 so there is already a built-in infinity. (In fact, there are several.) The following procedure just returns the floating point (positive) infinity directly.

> proc() Float(infinity) end();

Float(infinity)

There is also an exact infinity ("infinity"), a negative float infinity ("Float(-infinity)" or "-Float(infinity)") and a suite of complex infinities. The next procedure returns a boxed machine (double precision) float infinity.

> proc() HFloat(infinity) end();

HFloat(infinity)

## Mathematica / Wolfram Language[edit]

Mathematica has infinity built-in as a symbol. Which can be used throughout the software:

Sum[1/n^2,{n,Infinity}]

1/Infinity

Integrate[Exp[-x^2], {x, -Infinity, Infinity}]

10^100 < Infinity

gives back:

Pi^2/6 0 Sqrt[Pi] True

Moreover Mathematica has 2 other variables that represent 'infinity': DirectedInfinity[r] and ComplexInfinity. DirectInfinity[r] represents an infinite quantity with complex direction r. ComplexInfinity represents an infinite quantity with an undetermined direction; like 1/0. Which has infinite size but undetermined direction. So the general infinity is DirectedInfinity, however if the direction is unknown it will turn to ComplexInfinity, DirectedInfinity[-1] will return -infinity and DirectedInfinity[1] will return infinity. Directed infinity can, for example, be used to integrate over an infinite domain with a given complex direction: one might want to integrate Exp[-x^2]/(x^2-1) from 0 to DirectedInfinity[Exp[I Pi/4]]:

Integrate[Exp[-x^2]/(x^2 - 1), {x, 0, DirectedInfinity[Exp[I Pi/4]]}]

gives back:

-((Pi (I+Erfi[1]))/(2 E))

## MATLAB / Octave[edit]

MATLAB implements the IEEE 754 floating point standard as the default for all numeric data types. +Inf and -Inf are by default implemented and supported by MATLAB. To check if a variable has the value +/-Inf, one can use the built-in function "isinf()" which will return a Boolean 1 if the number is +/-inf.

a = +Inf;

isinf(a)

Returns:

ans = 1

## Maxima[edit]

/* Maxima has inf (positive infinity) and minf (negative infinity) */

declare(x, real)$

is(x < inf);

/* true */

is(x > minf);

/* true */

/* However, it is an error to try to divide by zero, even with floating-point numbers */

1.0/0.0;

/* expt: undefined: 0 to a negative exponent.

-- an error. To debug this try: debugmode(true); */

## Metafont[edit]

Metafont numbers are a little bit odd (it uses fixed binary arithmetic). For Metafont, the biggest number (and so the one which is also considered to be infinity) is 4095.99998. In fact, in the basic set of macros for Metafont, we can read

infinity := 4095.99998;

## Modula-2[edit]

MODULE inf;

IMPORT InOut;

BEGIN

InOut.WriteReal (1.0 / 0.0, 12, 12);

InOut.WriteLn

END inf.

Producing

[email protected]:~/modula/rosetta$ inf

**** RUNTIME ERROR bound check error

Floating point exception

## Modula-3[edit]

IEEESpecial contains 3 variables defining negative infinity, positive infinity, and NaN for all 3 floating point types in Modula-3 (REAL, LONGREAL, and EXTENDED).

If the implementation doesn't support IEEE floats, the program prints arbitrary values (Critical Mass Modula-3 implementation does support IEEE floats).

MODULE Inf EXPORTS Main;

IMPORT IO, IEEESpecial;

BEGIN

IO.PutReal(IEEESpecial.RealPosInf);

IO.Put("\n");

END Inf.

Output:

Infinity

## Nemerle[edit]

Both single and double precision floating point numbers support PositiveInfinity, NegativeInfinity and NaN.

def posinf = double.PositiveInfinity;

def a = IsInfinity(posinf); // a = true

def b = IsNegativeInfinity(posinf); // b = false

def c = IsPositiveInfinity(posinf); // c = true

## Nim[edit]

Inf

is a predefined constant in Nim:

var f = Inf

echo f

## NS-HUBASIC[edit]

10 PRINT 1/0

- Output:

?DZ ERROR is a division by zero error in NS-HUBASIC.

?DZ ERROR IN 10

## OCaml[edit]

infinity

is already a pre-defined value in OCaml.

# infinity;; - : float = infinity # 1.0 /. 0.0;; - : float = infinity

## Oforth[edit]

10 1000.0 powf dup println dup neg println 1 swap / println

- Output:

1.#INF -1.#INF 0

## Ol[edit]

Inexact numbers support can be disabled during recompilation using "-DOLVM_INEXACTS=0" command line argument. Inexact numbers in Ol demands the existence of infinity, by demanding IEEE numbers. There are two signed infinity numbers (as constants) in Ol:

+inf.0 ; positive infinity -inf.0 ; negative infinity

(define (infinite? x) (or (equal? x +inf.0) (equal? x -inf.0)))

(infinite? +inf.0) ==> #true

(infinite? -inf.0) ==> #true

(infinite? +nan.0) ==> #false

(infinite? 123456) ==> #false

(infinite? 1/3456) ==> #false

(infinite? 17+28i) ==> #false

## OpenEdge/Progress[edit]

The unknown value (represented by a question mark) can be considered to equal infinity. There is no difference between positive and negative infinity but the unknown value sometimes sorts low and sometimes sorts high when used in queries.

MESSAGE

1.0 / 0.0 SKIP

-1.0 / 0.0 SKIP(1)

( 1.0 / 0.0 ) = ( -1.0 / 0.0 )

VIEW-AS ALERT-BOX.

Output

--------------------------- Message (Press HELP to view stack trace) --------------------------- ? ? yes --------------------------- OK Help ---------------------------

## OxygenBasic[edit]

Using double precision floats:

print 1.5e-400 '0

print 1.5e400 '#INF

print -1.5e400 '#-INF

print 0/-1.5 '-0

print 1.5/0 '#INF

print -1.5/0 '#-INF

print 0/0 '#qNAN

function f() as double

return -1.5/0

end function

print f '#-INF

## Oz[edit]

declare

PosInf = 1./0.

NegInf = ~1./0.

in

{Show PosInf}

{Show NegInf}

%% some assertion

42. / PosInf = 0.

42. / NegInf = 0.

PosInf * PosInf = PosInf

PosInf * NegInf = NegInf

NegInf * NegInf = PosInf

## PARI/GP[edit]

`+oo`

infty()={

[1] \\ Used for many functions like intnum

};

## Pascal[edit]

See Delphi

## Perl[edit]

Positive infinity:

my $x = 0 + "inf";

my $y = 0 + "+inf";

Negative infinity:

my $x = 0 - "inf";

my $y = 0 + "-inf";

The "`0 + `

..." is used here to make sure that the variable stores a value that is actually an infinitive number instead of just a string `"inf"`

but in practice one can use just:

my $x = "inf";

and `$x`

while originally holding a string will get converted to an infinite number when it is first used as a number.

Some programmers use expressions that overflow the IEEE floating point numbers such as:

my $x = 1e1000;

which is 10^{1000} or googol^{10} or even numbers like this one:

my $y = 10**10**10;

which is 10^{10000000000} but it has to make some assumptions about the underlying hardware format and its size. Furthermore, using such literals in the scope of some pragmas such as `bigint`

, `bignum`

or `bigrat`

would actually compute those numbers:

use bigint;

my $x = 1e1000;

my $y = 10**10**10; # N.B. this will consume vast quantities of RAM

Here the `$x`

and `$y`

when printed would give 1001 and 10000000001-digit numbers respectively, the latter taking no less than 10GB of space to just output.

Under those pragmas, however, there is a simpler way to use infinite values, thanks to the `inf`

symbol being exported into the namespace by default:

use bigint;

my $x = inf;

my $y = -inf;

## Perl 6[edit]

Inf support is required by language spec on all abstract Numeric types (in the absence of subset constraints) including Num, Rat and Int types. Native integers cannot support Inf, so attempting to assign Inf will result in an exception; native floats are expected to follow IEEE standards including +/- Inf and NaN.

my $x = 1.5/0; # Failure: catchable error, if evaluated will return: "Attempt to divide by zero ...

my $y = (1.5/0).Num; # assigns 'Inf'

## Phix[edit]

constant infinity = 1e300*1e300

? infinity

- Output:

inf

## PHP[edit]

This is how you get infinity:

INF

Unfortunately, "1.0 / 0.0" doesn't evaluate to infinity; but instead seems to evaluate to False, which is more like 0 than infinity.

PHP has functions is_finite() and is_infinite() to test for infiniteness.

## PL/I[edit]

declare x float, y float (15), z float (18);

put skip list (huge(x), huge(y), huge(z));

## PicoLisp[edit]

The symbol 'T' is used to represent infinite values, e.g. for the length of circular lists, and is greater than any other value in comparisons. PicoLisp has only very limited floating point support (scaled bignum arithmetics), but some functions return 'T' for infinite results.

(load "@lib/math.l")

: (exp 1000.0)

-> T

## PostScript[edit]

/infinity { 9 99 exp } def

## PowerShell[edit]

A .NET floating-point number representing infinity is available.

function infinity {

[double]::PositiveInfinity

}

## PureBasic[edit]

PureBasic uses IEEE 754 coding for float types. PureBasic also includes the function `Infinity()` that return the positive value for infinity and the boolean function `IsInfinite(value.f)` that returns true if the floating point value is either positive or negative infinity.

If OpenConsole()

Define.d a, b

b = 0

;positive infinity

PrintN(StrD(Infinity())) ;returns the value for positive infinity from builtin function

a = 1.0

PrintN(StrD(a / b)) ;calculation results in the value of positive infinity

;negative infinity

PrintN(StrD(-Infinity())) ;returns the value for negative infinity from builtin function

a = -1.0

PrintN(StrD(a / b)) ;calculation results in the value of negative infinity

Print(#crlf$ + #crlf$ + "Press ENTER to exit"): Input()

CloseConsole()

EndIf

*Outputs*

+Infinity +Infinity -Infinity -Infinity

## Python[edit]

This is how you get infinity:

>>> float('infinity')

inf

*Note: When passing in a string to float(), values for NaN and Infinity may be returned, depending on the underlying C library. The specific set of strings accepted which cause these values to be returned depends entirely on the underlying C library used to compile Python itself, and is known to vary.*

*The Decimal module explicitly supports +/-infinity Nan, +/-0.0, etc without exception.*

Floating-point division by 0 doesn't give you infinity, it raises an exception:

>>> 1.0 / 0.0

Traceback (most recent call last):

File "<stdin>", line 1, in <module>

ZeroDivisionError: float division

If `float('infinity')` doesn't work on your platform, you could use this trick:

>>> 1e999 1.#INF

It works by trying to create a float bigger than the machine can handle.

## R[edit]

Inf #positive infinity

-Inf #negative infinity

.Machine$double.xmax # largest finite floating-point number

is.finite # function to test to see if a number is finite

# function that returns the input if it is finite, otherwise returns (plus or minus) the largest finite floating-point number

forcefinite <- function(x) ifelse(is.finite(x), x, sign(x)*.Machine$double.xmax)

forcefinite(c(1, -1, 0, .Machine$double.xmax, -.Machine$double.xmax, Inf, -Inf))

# [1] 1.000000e+00 -1.000000e+00 0.000000e+00 1.797693e+308

# [5] -1.797693e+308 1.797693e+308 -1.797693e+308

## Racket[edit]

as in Scheme:

#lang racket

+inf.0 ; positive infinity

(define (finite? x) (< -inf.0 x +inf.0))

(define (infinite? x) (not (finite? x)))

## REXX[edit]

The language specifications for REXX are rather open-ended when it comes to language limits.

Limits on numbers are expressed as: The REXX interpreter has to at **least** handle exponents up to nine (decimal) digits.

So it's up to the writers of the REXX interpreter to decide what limits are to be implemented or enforced.

For the default setting of NUMERIC DIGITS 9 the biggest number that can be used is (for the Regina REXX and R4 REXX interpreters): .999999999e+999999999

For a setting of NUMERIC DIGITS 100 the biggest number that can be used is: (for the Regina REXX interpreter) .9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999e+999999999 (for the R4 REXX interpreter) .9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999e+9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 ... and so on with larger NUMERIC DIGITS

For most REXX interpreters, the maximum number of digits is only limited by virtual storage,

but the pratical limit would be a little less than half of available virtual storage,

which would (realistically) be around one billion digits. Other interpreters have a limitation of roughly 8 million digits.

## RLaB[edit]

>> x = inf()

inf

>> isinf(x)

1

>> inf() > 10

1

>> -inf() > 10

0

## Ruby[edit]

Infinity is a Float value

a = 1.0/0 # => Infinity

a.finite? # => false

a.infinite? # => 1

a = -1/0.0 # => -Infinity

a.infinite? # => -1

a = Float::MAX # => 1.79769313486232e+308

a.finite? # => true

a.infinite? # => nil

a = Float::INFINITY # => Infinity

## Rust[edit]

Rust has builtin function for floating types which returns infinity. This program outputs 'inf'.

fn main() {

let inf = std::f32::INFINITY;

println!("{}", inf);

}

## Scala[edit]

**See also**

In order to be compliant with IEEE-754, Scala has all support for infinity on its floating-point types (`float`, `double`). You can get infinity from constants in the corresponding wrapper class; for example, `Double`:

val inf = Double.PositiveInfinity //defined as 1.0/0.0

inf.isInfinite; //true

The largest possible number in Scala (without using the `Big` classes) is also in the `Double` class.

val biggestNumber = Double.MaxValue

REPL session:

scala> 1 / 0.

res2: Double = Infinity

scala> -1 / 0.

res3: Double = -Infinity

scala> 1 / Double.PositiveInfinity

res4: Double = 0.0

scala> 1 / Double.NegativeInfinity

res5: Double = -0.0

## Scheme[edit]

+inf.0 ; positive infinity

(define (finite? x) (< -inf.0 x +inf.0))

(define (infinite? x) (not (finite? x)))

## Seed7[edit]

Seed7s floating-point type (float) supports infinity. The library float.s7i defines the constant Infinity as:

const float: Infinity is 1.0 / 0.0;

Checks for infinity can be done by comparing with this constant.

## Sidef[edit]

var a = 1.5/0 # Inf

say a.is_inf # true

say a.is_pos # true

var b = -1.5/0 # -Inf

say b.is_ninf # true

say b.is_neg # true

var inf = Inf

var ninf = -Inf

say (inf == -ninf) # true

## Slate[edit]

PositiveInfinity

## Smalltalk[edit]

Each of the finite-precision Float classes (FloatE, FloatD, FloatQ), have an "infinity" method that returns infinity in that type.

st> FloatD infinity Inf st> 1.0 / 0.0 Inf

The class names are different (Float, ShortFloat and LongFloat); for sourcecode compatibility, you can do "Smalltalk at:#FloatQ put:LongFloat". The behavior is slightly different, in that an exception is raised:

Float infinity -> INF

1.0 / 0.0 -> "ZeroDivide exception"

but we can simulate the other behavior with:

[

1.0 / 0.0

] on: ZeroDivide do:[:ex |

ex proceedWith: (Float infinity)

]

-> INF

## Standard ML[edit]

Real.posInf

- Real.posInf; val it = inf : real - 1.0 / 0.0; val it = inf : real

## Swift[edit]

Swift's floating-point types (`Float`, `Double`, and any other type that conforms to the `FloatingPointNumber` protocol) all support infinity. You can get infinity from the `infinity` class property in the type:

let inf = Double.infinity

inf.isInfinite //true

As a function:

func getInf() -> Double {

return Double.infinity

}

## Tcl[edit]

Tcl 8.5 has Infinite as a floating point value, not an integer value

package require Tcl 8.5

expr {1.0 / 0} ;# ==> Inf

expr {-1.0 / 0} ;# ==> -Inf

expr {inf} ;# ==> Inf

expr {1 / 0} ;# ==> "divide by zero" error; Inf not part of range of integer division

A maximal integer is not easy to find, as Tcl switches to unbounded integers when a 64-bit integer is about to roll over:

% format %lx -1 ;# all bits set

ffffffffffffffff

% regsub f 0x[format %lx -1] 7 ;# unset the sign bit for positive

0x7fffffffffffffff

% set ii [expr [regsub f 0x[format %lx -1] 7]] ;# show as decimal

9223372036854775807

% incr ii

9223372036854775808 ;# silently upgrade to unbounded integer, still positive

A theoretical MAXINT, though very impractical, could be

string repeat 9 [expr 2**32-1]

## TI-89 BASIC[edit]

∞

## TorqueScript[edit]

function infinity()

{

return 1/0;

}

## Trith[edit]

The following functions are included as part of the core operators:

: inf 1.0 0.0 / ;

: -inf inf neg ;

: inf? abs inf = ;

## Ursa[edit]

Infinity is a defined value in Ursa.

decl double d

set d Infinity

## Ursala[edit]

IEEE double precision floating point numbers are a primitive type in Ursala. This function returns IEEE double precision infinity when applied to any argument, using the value inf, which is declared as a constant in the flo library.

#import flo

infinity = inf!

## Visual Basic[edit]

Positive infinity, negative infinity and indefinite number (usable as NaN) can be generated by deliberately dividing by zero under the influence of `On Error Resume Next`

:

Option Explicit

Private Declare Sub GetMem8 Lib "msvbvm60.dll" _

(ByVal SrcAddr As Long, ByVal TarAddr As Long)

Sub Main()

Dim PlusInfinity As Double

Dim MinusInfinity As Double

Dim IndefiniteNumber As Double

On Error Resume Next

PlusInfinity = 1 / 0

MinusInfinity = -1 / 0

IndefiniteNumber = 0 / 0

Debug.Print "PlusInfinity = " & CStr(PlusInfinity) _

& " (" & DoubleAsHex(PlusInfinity) & ")"

Debug.Print "MinusInfinity = " & CStr(MinusInfinity) _

& " (" & DoubleAsHex(MinusInfinity) & ")"

Debug.Print "IndefiniteNumber = " & CStr(IndefiniteNumber) _

& " (" & DoubleAsHex(IndefiniteNumber) & ")"

End Sub

Function DoubleAsHex(ByVal d As Double) As String

Dim l(0 To 1) As Long

GetMem8 VarPtr(d), VarPtr(l(0))

DoubleAsHex = Right$(String$(8, "0") & Hex$(l(1)), 8) _

& Right$(String$(8, "0") & Hex$(l(0)), 8)

End Function

- Output:

PlusInfinity = 1,#INF (7FF0000000000000)MinusInfinity = -1,#INF (FFF0000000000000) IndefiniteNumber = -1,#IND (FFF8000000000000)

## Yabasic[edit]

infinity = 1e300*1e300

if str$(infinity) = "inf" print "Infinity"

## zkl[edit]

zkl doesn't like INF, NaN, etc but sorta knows about them:

1.5/0

- Output:

Exception thrown: MathError(INF (number is infinite))

## ZX Spectrum Basic[edit]

ZX Spectrum BASIC has no infinity handling;PRINT 1/0will be met with

6 Number too big, 0:1

A quick doubling loop will get you halfway to the maximum floating point value:

10 LET z=1

20 PRINT z

30 LET z=z*2

40 GO TO 20

Output will end with:

4.2535296E+37 8.5070592E+37 6 Number too big, 30:1

Precision has been lost by this stage through the loop, but one more manual double and subtract 1 will get you the true displayable maximum of 1.7014118E+38 (or 2^127-1).

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